Divalent cations have been reported to develop bridges between anionic polyelectrolytes and negatively-charged colloidal particles, thereby enhancing particle flocculation. However, results from this study of kaolinite suspensions dosed with various anionic polyacrylamides (PAMs) reveal that Ca2+ and Mg2+ can lead to colloid stabilization under some conditions. To explain the opposite but coexisting processes of flocculation and stabilization with divalent cations, a conceptual flocculation model with (1) particle-binding divalent cationic bridges between PAM molecules and kaolinite particles and (2) polymer-binding divalent cationic bridges between PAM molecules is proposed. The particle-binding bridges enhanced flocculation and aggregated kaolinite particles in large, easily-settleable flocs whereas the polymer-binding bridges increased steric stabilization by developing polymer layers covering the kaolinite surface. Both the particle-binding and polymer-binding divalent cationic bridges coexist in anionic PAM- and kaolinite-containing suspensions and thus induce the counteracting processes of particle flocculation and stabilization. Therefore, anionic polyelectrolytes in divalent cation-enriched aqueous solutions can sometimes lead to the stabilization of colloidal particles due to the polymer-binding divalent cationic bridges. Display omitted ► Effects of divalent cations on kaolinite flocculation and stabilization are compared for different anionic polyacrylamides. ► Particle stabilization results from surface coatings formed via polyelectrolyte-binding divalent cationic bridges. ► Polyelectrolyte-binding divalent cationic bridges inhibit kaolinite flocculation primarily by steric stabilization. ► Competition between particle-binding and polyelectrolyte-binding bridges explains kaolinite flocculation or stabilization.